State the claim and its opposite and the null and alternate hypotheses, the type

Question

State the claim and its opposite and the null and alternate hypotheses, the type of analysis that should be performed (either testing inferences about two proportions, means from independent samples, or means from matched pairs), and the formula used to calculate the test statistic. Show the values substituted into the formula, and calculate the value of the test statistic, draw and label a graph, determine the P-value, state what to do with the null hypothesis, and use the flow chart to state your conclusion. Assume that the samples are simple random samples and all requirements are satisfied.

1. To illustrate the effects of driving under the influence (DUI) of alcohol, a police officer brought a DUI simulator to a local high school. Student reaction time in an emergency was measured with unimpaired vision and also while wearing a pair of special goggles to simulate the effects of alcohol on vision. For a sample of nine teenagers, the time (in seconds) required to bring the vehicle to a stop from a speed of 60 miles per hour was recorded. Assume that differences are computed as impaired minus normal. Test the claim by the teens that there is no difference in reaction times. Subject: 1 2 3 4 5 6 7 8 9 Impaired: 5.77 5.67 5.51 5.32 5.83 5.49 5.23 5.61 5.63 in sec Normal: 4.47 4.24 4.58 4.65 4.31 4.80 4.55 5.00 4.79 in sec

Explanation / Answer

State the Claim :

There is significant impact on student reaction time in an emergency when with impaired vision of special goggles to simulate effects of alcohol on vision and when there is no impaired vision. For opposite there is no impact on student reaction time in an emergency when   with impaired vision of special goggles to simulate effects of alcohol on vision.

Null Hypothesis : H0 : There is no difference in student reaction time in both conditions. impaired = Normal

ALternative Hypothesis : Ha : There is no difference in student reaction time in both conditions. impaired Normal

We will do t - test for matched pairs.

Test - Statistics

t = [(ximpaired - xNormal) - (impaired - Normal)] / (sd/ n)

sd = 0.36/ 9 = 0.12

t = ( 5.56 - 4.60)/ 0.12 = 8

dF = n -1 = 8

so tcritical = 2.306

P - value = 0.0000406

Subject Impaired Paired 1 5.77 4.47 2 5.67 4.24 3 5.51 4.58 4 5.32 4.65 5 5.83 4.31 6 5.49 4.80 7 5.23 4.55 8 5.61 5.00 9 5.63 4.79

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